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Fuzzy adaptive output feedback control for MIMO nonlinear systems. (English) Zbl 1082.93032
Summary: Two observer-based adaptive fuzzy output feedback control schemes are presented for a class of uncertain continuous-time multi-input–multi-output (MIMO) nonlinear dynamics systems whose states are not available. Within these schemes, fuzzy logic systems are employed to approximate the plant’s unknown nonlinear functions and then the state observer is designed for estimating the states of the plant, upon which a fuzzy adaptive output feedback controller is firstly investigated. In order to overcome the controller singularity problem and relax the requirement of bounding parameter values, a second modified fuzzy adaptive output feedback controller is proposed by using a regularized inverse and a robustifying control term. All parameter adaptive laws and robustifying control terms are derived based on Lyapunov stability analysis, so that convergence to zero of tracking errors and boundedness of all signals in the closed-loop system can be guaranteed. Simulations performed on a two-link robot manipulator illustrate the approach and exhibit its performance.

MSC:
93C42 Fuzzy control/observation systems
93C40 Adaptive control/observation systems
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[1] Chang, Y.C., Robust tracking control for nonlinear MIMO systems via fuzzy approaches, Automatica, 36, 1535-1545, (2000) · Zbl 0967.93060
[2] Chen, B.S.; Lee, C.H.; Chang, Y.C., \(H^\infty\) tracking design of uncertain nonlinear SISO systems: adaptive fuzzy approach, IEEE trans. fuzzy systems, 3, 4, 32-43, (1994)
[3] Kanellakopoulos, I.; Kokotovic, P.V.; Morse, A.S., Systematic design of adaptive controllers for feedback linearizable systems, IEEE trans. automat. control, 36, 1241-1253, (1991) · Zbl 0768.93044
[4] Krstic, M.; Kanellakopoulos, I.; Kokotovic, P.V., Nonlinear and adaptive control design, (1995), Wiley New York · Zbl 0763.93043
[5] Li, H.X.; Tong, S.C., A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems, IEEE trans. fuzzy systems, 11, 1, 24-35, (2003)
[6] Ordonez, R.; Passino, K.M., Stable multi-output adaptive fuzzy/neural control, IEEE trans. fuzzy systems, 4, 32-43, (1999)
[7] Sastry, S.S.; Bodson, M., Adaptive control: stability, convergence, and robustness, (1989), Prentice-Hall Englewood Cliffs, NJ · Zbl 0721.93046
[8] Sastry, S.S.; Isidori, A., Adaptive control of a class of nonlinear systems, IEEE trans. automat. control, 34, 1123-1131, (1989) · Zbl 0693.93046
[9] Slotine, J.E.; Li, W., Applied nonlinear control, (1991), Prentice-Hall Englewood Cliffs, NJ · Zbl 0753.93036
[10] Spooner, J.T.; Passino, K.M., Stable adaptive control of a class of nonlinear systems and neural network, IEEE trans. fuzzy systems, 4, 339-359, (1996)
[11] Su, C.Y.; Stepanenko, Y., Adaptive control of a class of nonlinear systems with fuzzy logic, IEEE trans. fuzzy systems, 3, 339-359, (1994)
[12] Tong, S.C.; Chai, T.Y., Fuzzy adaptive control for a class of nonlinear systems, Fuzzy sets and systems, 101, 31-39, (1999) · Zbl 0952.93077
[13] Tong, S.C.; Tang, J.T.; Wang, T., Fuzzy adaptive control of multivariable nonlinear systems, Fuzzy sets and systems, 111, 153-167, (2000) · Zbl 0976.93049
[14] Tong, S.C.; Wang, T.; Tang, J.T., Fuzzy adaptive output tracking control of nonlinear systems, Fuzzy sets and systems, 111, 169-182, (2000) · Zbl 0976.93050
[15] Wang, L.X., Stable adaptive fuzzy control of nonlinear systems, IEEE trans. fuzzy systems, 1, 2, 32-43, (1993)
[16] Wang, L.X., Adaptive fuzzy systems and control: design and stability, (1994), Prentice-Hall Englewood Cliffs, NJ
[17] Yin-Guang Leu; Tsu-Tian Lee; Wei-Yen Wang, Observer-based adaptive fuzzy-neural control for unknown nonlinear dynamical systems, IEEE trans. systems man cybernet., 29, 583-591, (1999)
[18] Zhang, H.G.; Bie, Z.B., Adaptive fuzzy control of MIMO nonlinear systems, Fuzzy sets and systems, 115, 191-204, (2000) · Zbl 0960.93024
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